What is the solution for y(dy)/(dx)= x/((x+1)) ?

The solution for y(dy)/(dx)= x/((x+1)) is y=sqrt(2x+2-2ln(x+1)+c_{1)},y=-sqrt(2x+2-2ln(x+1)+c_{1)}

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y(dy)/(dx)= x/((x+1))

y \frac{d y}{d x} = \frac{x}{( x + 1 )}

y = 2 x + 2 - 2 ln (x + 1) + c_{1}, y = - 2 x + 2 - 2 ln (x + 1) + c_{1}

Solution steps

y \frac{d y}{d x} = \frac{x}{( x + 1 )}

Solve separable ODE:

y = 2 x + 2 - 2 ln (x + 1) + c_{1}, y = - 2 x + 2 - 2 ln (x + 1) + c_{1}

y = 2 x + 2 - 2 ln (x + 1) + c_{1}, y = - 2 x + 2 - 2 ln (x + 1) + c_{1}

\frac{d y}{d x} = - 4 x y^{2}, y (0) = 1

\frac{d P}{d t} = - e^{- t} P, P (0) = 100

y^{^{'}} = y^{\frac{1}{5}}

\frac{d y}{d x} (1 - x) = y^{2}

\frac{d y}{d x} y = arccos (\frac{1}{x})

What is the solution for y(dy)/(dx)= x/((x+1)) ?
The solution for y(dy)/(dx)= x/((x+1)) is y=sqrt(2x+2-2ln(x+1)+c_{1)},y=-sqrt(2x+2-2ln(x+1)+c_{1)}